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Name ________________________________________ Date __________________ Class__________________ LESSON 4-2 Reteach Classifying Triangles You can classify triangles by their angle measures. An equiangular triangle, for example, is a triangle with three congruent angles. Examples of three other triangle classifications are shown in the table. Acute Triangle all acute angles Right Triangle Obtuse Triangle ∠JKL is obtuse so UJLK is an obtuse triangle. one obtuse angle one right angle You can use angle measures to classify ΔJML at right. ∠JLM and ∠JLK form a linear pair, so they are supplementary. m∠JLM + m∠JLK = 180° Def. of supp. � m∠JLM + 120° = 180� Substitution m∠JLM = 60° Subtract. Since all the angles in UJLM are congruent, UJLM is an equiangular triangle. Classify each triangle by its angle measures. 1. 2. ________________________ 3. _________________________ ________________________ Use the figure to classify each triangle by its angle measures. 4. UDFG ________________________ 5. UDEG ________________________ 6. UEFG ________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 4-14 Holt McDougal Geometry Name ________________________________________ Date __________________ Class__________________ LESSON 4-2 Reteach Classifying Triangles continued You can also classify triangles by their side lengths. Equilateral Triangle Isosceles Triangle Scalene Triangle all sides congruent at least two sides congruent no sides congruent You can use triangle classification to find the side lengths of a triangle. Step 1 Find the value of x. QR = RS 4x = 3x + 5 x=5 Step 2 Def. of > segs. Substitution Simplify. Use substitution to find the length of a side. 4x = 4(5) = 20 Substitute 5 for x. Simplify. Each side length of UQRS is 20. Classify each triangle by its side lengths. 7. UEGF ________________________ 8. UDEF ________________________ 9. UDFG ________________________ Find the side lengths of each triangle. 10. 11. _________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 4-15 Holt McDougal Geometry Practice C Challenge 1. 228 ft 8 in. 1. 16 3. 3 5. 27 2. 83 ft 2 in. 3. For UABC, x = 1 or −1 because the triangles are isosceles, x2 = 1, so x = ±1. For UDEF, x ≠ −1 because a length cannot be negative, and if x = −1 then EF = −1. So x = 1 is the only solution for UDEF. 4. UABC must be isosceles and UDEF must be an equilateral triangle. 5. GH = GI = 25, HI = 9; GH = GI = 9, HI = 1 6. Possible answer: By the Corr. Angles Postulate, m∠A = m∠21 = m∠23 = 60° and m∠G = m∠14 = m∠24 = 60°. Construct a line parallel to CE through D. Then also by the Corr. Angles Postulate, m∠D = m∠22 = m∠1 = m∠15 = m∠12 = 60°. By the definition of a straight angle and the Angle Add. Postulate, m∠1 + m∠4 + m∠21 = 180°, but m∠1 = m∠21 = m∠A = 60°. Therefore by substitution and the Subt. Prop. of Equality, m∠4 = 60°. Similar reasoning will prove that m∠11 = m∠18 = m∠19 = 60°. By the Alt. Int. Angles Theorem, m∠19 = m∠20 and m∠18 = m∠16. m∠20 = m∠10 and m∠16 = m∠5 by the Vertical Angles Theorem. By the Alt. Int. Angles Theorem, m∠4 = m∠2 and m∠5 = m∠7 and m∠10 = m∠8 and m∠11 = m∠13. By the definition of a straight angle, the Angle Addition Postulate, substitution, and the Subt. Prop., m∠17 = m∠6 = m∠3 = m∠9. Substitution will show that the measure of every angle is 60. Because every angle has the same measure, all of the angles are congruent by the definition of congruent angles. Reteach 1. 3. 5. 7. 9. 11. right acute acute isosceles isosceles 7; 7; 4 2. 4. 6. 8. 10. obtuse right obtuse scalene 9; 9; 9 2. 7 4. 1 6. 21 = 57 7. 8. = 12 9. = 21 10. = 36 11. Answers will vary. Problem Solving 1. 3 frames 2. 4 3 3 1 ft; 4 ft; 5 ft 8 8 4 3. Santa Fe and El Paso, 427 km; El Paso and Phoenix, 561 km; Phoenix and Santa Fe, 609 km 4. scalene 5. B 6. J Reading Strategies 1. scalene, obtuse 2. equilateral, equiangular, acute 3. isosceles, right 4. isosceles triangle 5. no such triangle 6. scalene right triangle 4-3 ANGLE RELATIONSHIPS IN TRIANGLES Practice A 1. ∠1, ∠4, ∠6 2. ∠2, ∠3 3. ∠2, ∠3, ∠5 4. equiangular 5. 180° 6. right Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A34 Holt McDougal Geometry